Classification commonly refers to an operation for classifying particles having different diameters by their diameters. Countercurrent classification or selection tube classification is a type of classification technique, and is characterized in causing a liquid in which particles are suspended to flow upward (or placing particles into an upward flowing fluid) through a classification tube or a selection tube that is arranged in the vertical direction (see Patent Documents 1 and 2).
FIGS. 8(a) to 8(c) are diagrams illustrating the principle of countercurrent classification or selection tube classification. Typically, a classification or selection tube 10 for use in the countercurrent classification or selection tube classification has a tapered shape or an inverted-conical shape such that the cross-sectional area of the flow path increases as it goes vertically upward. In the examples shown in FIGS. 8(a) to 8(c), the classification tube 10 has an inverted-conical shape, and is arranged in the vertical direction. A fluid (or liquid) is caused to flow vertically upward through the classification tube 10. If the velocity (or flow rate) distribution of the fluid is substantially uniform or constant within a horizontal plane (and if the variation in the flow rate in the classification tube 10 over time can be disregarded), the flow rate of the fluid decreases as the diameter of the flow path, or the cross-sectional area, of the classification tube 10 increases, that is, as the fluid rises in the vertical direction.
When a mixture containing first particles having a particle diameter a1 and a density ρ1 (indicated by black circles) and second particles having a particle diameter a2 and a density ρ2 (indicated by white circles) are suspended in a fluid, and the fluid is caused to flow through the classification tube 10 as shown in FIG. 8(a), particles contained in the fluid flowing through the classification tube 10 are subjected to the gravitational force and the buoyancy force as well as the fluid resistance force, or so-called drag force, which is proportional to a difference between the flow rate and the particle velocity. A force F, in the vertical direction (i.e., z direction) that acts on each of the particles contained in the fluid flowing through the classification tube 10 is given as follows (where the vertically downward direction is taken as positive):Fz=4/3πai3(ρi−ρ0)g−6πηai(vf−vpi)where g is the acceleration of the gravitational force, ai is the diameter of the particles, ρ1 is the density of the particles, ρ0 is the density of the fluid (or liquid), η is the viscosity coefficient of the fluid, vf is the velocity of the fluid, and vpi is the velocity of the particles. Note that the index i is 1 or 2, and is used for distinguishing between the parameters of the first particles and the parameters of the second particles.
By adjusting the shape of the classification tube 10 or the flow rate of the fluid that flows through the classification tube 10 so that Fz=0 is met with respect to both the first particles and the second particles in the classification tube 10 (i.e., so that the drag force, the gravitational force, and the buoyancy force that act on the particles balance out or cancel out in the classification tube 10), the first particles and the second particles float (in a stable manner) at a height where Fz=0. If the first particles and the second particles are made of the same substances (if ρ1=ρ2), the height where Fz=0, that is, the height at which the particles float differs according to the diameter of the particles. For example, if a1<a2, the first particles float in the classification tube 10 at a position that is higher than the height at which the second particles float, as shown in FIG. 8(b). The fluid velocity of at the height at which the first particles float is lower than the fluid velocity vf at the height at which the second particles float. Furthermore, in the case where the mixture is introduced from outside the classification tube 10 into a fluid flowing upward through the classification tube 10 as with the classification apparatuses disclosed in Patent Documents 1 and 2, by adjusting the flow rate of the fluid flowing through the classification tube 10 so that Fz<0 is met with respect to the first particles and Fz>0 is met with respect to the second particles, it is possible to separate the first particles and the second particles and to collect the respective types of particles from the upper end and the lower end of the classification tube 10.
Accordingly, the particles of the same type (i.e. particles made of the same substance) that have different sizes are separated or classified according to particle diameter using the classification tube 10. As can be seen from the above equation, since the force Fz in the vertical direction that acts on the particles also depends on the density ρi of the particles, the height at which the particles in the classification tube 10 float and the direction in which the particles move also depend on the density ρi of the particles. Therefore, by suspending, in a fluid, a mixture containing, for example, multiple types of particles that have different densities, that is, multiple types of particles made of different substances, and causing the fluid to flow upward through the classification tube 10, it is possible to separate these particles by type.